On Sex, Evolution, and the Multiplicative Weights Update Algorithm
This work addresses a theoretical gap in evolutionary biology and algorithmic game theory by generalizing a model linking sex and MWUA, but it is incremental as it builds on prior results.
The paper tackles the problem of modeling sexual evolution as the multiplicative weights update algorithm (MWUA) by eliminating the need for weak selection and product distribution assumptions, showing that marginal allele distributions match MWUA in a general setting. It revises earlier claims, concluding that sexual dynamics do not imply additional properties beyond convergence.
We consider a recent innovative theory by Chastain et al. on the role of sex in evolution [PNAS'14]. In short, the theory suggests that the evolutionary process of gene recombination implements the celebrated multiplicative weights updates algorithm (MWUA). They prove that the population dynamics induced by sexual reproduction can be precisely modeled by genes that use MWUA as their learning strategy in a particular coordination game. The result holds in the environments of \emph{weak selection}, under the assumption that the population frequencies remain a product distribution. We revisit the theory, eliminating both the requirement of weak selection and any assumption on the distribution of the population. Removing the assumption of product distributions is crucial, since as we show, this assumption is inconsistent with the population dynamics. We show that the marginal allele distributions induced by the population dynamics precisely match the marginals induced by a multiplicative weights update algorithm in this general setting, thereby affirming and substantially generalizing these earlier results. We further revise the implications for convergence and utility or fitness guarantees in coordination games. In contrast to the claim of Chastain et al.[PNAS'14], we conclude that the sexual evolutionary dynamics does not entail any property of the population distribution, beyond those already implied by convergence.